How about 'dilute' or 'abridge'? Neither mean what you're asking for literally but I imagine one could use either by some creative license but it depends on your field.
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MussriDec 15 '12 at 8:30

While this technically belongs to English.se, it seems nobody here is sending anyone there anymore... The chance to get the answer here is better...
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SF.Dec 15 '12 at 12:41

There's also a 'joke verb' that's been circulating in my study group lately that might work if you know the reader would get it and if the writing is on the far right end of the formal/informal scale of language. The word is: "fermicalc" and I'll leave it to you to figure out how it came about.
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MussriDec 18 '12 at 10:05

3 Answers
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You are talking about oversimplification or misrepresentation. I think oversimplification is probably the best choice to replace reduce, but you would have to alter the construction of the sentence slightly to make it work. For example,

"Oversimplifying social problems by attributing them to bad media influence on disturbed kids is basically ignoring the main root of the problem and putting the fault on the media."

Or, to use the active voice,

"Attributing social problems to bad media influence on disturbed kids oversimplifies the problem, ignores the root cause, and puts the fault on the media."

I think "Oversimplification ... through reducing" would be best - you remove all other causes by reducing the problem to this single one, which comprises oversimplification of the whole.
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SF.Dec 15 '12 at 13:11

I don't know about that. Simplify means "to reduce". How would you re-phrase the sentence?
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tylerharmsDec 15 '12 at 13:31

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But there's no word "overreduce". "Oversimplification" is a loaded word that carries the meaning "it is something bad". "Reducing" is a neutral verb for the specific action that, being performed recklessly, leads to the problem. So, taking your first sequence I'd change the beginning: "Oversimplification of social problems by reducing them to bad media influence..." I'd also stuff a "scapegoat" somewhere near the end, but that's just me being me.
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SF.Dec 15 '12 at 14:20

I agree about the somewhat pejorative connotation of oversimplify. I got the impression, though, that the OP was heading in that direction with the use of "basically" in his example sentence.
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tylerharmsDec 16 '12 at 22:14

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maybe I didn't make myself clear: using a pejorative/loaded word is perfectly acceptable if you express a negative opinion. It's not the same as a vulgar/obscene word after all!
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SF.Dec 16 '12 at 22:59